Algebraic Geometry Seminar: How should maximal orders move?

  • Date: 03/15/2010
Max Lieblich (University of Washington)

University of British Columbia


I will discuss joint work in progress with Rajesh Kulkarni
on the moduli of maximal orders on surfaces. In contrast to the
"classical" case of Azumaya algebras, ramified maximal orders have
several potentially interesting moduli spaces. I will discuss three
different scheme structures on the same set of points: a naive
structure, a structure arising from a non-commutative version of
Koll\'ar's condition on moduli of stable surfaces, and a structure
that comes from hidden Azumaya algebras on stacky models of the
underlying surface. Only (?) the third admits a natural
compactification carrying a virtual fundamental class, giving rise to
potentially new numerical invariants of division algebras over
function fields of surfaces.


3:10 - 4:30pm, WMAX 110.